正规互质因子扰动模型集的闭环辨识与检验

鲁棒控制的系统辨识问题是控制领域一个十分活跃的研究方向。该文综述了具有正规互质因子扰动模型集的辨识与检验的结果。在闭环实验数据已知时 ,给出了正规互质因子频域响应极大似然估计的解析表达式 ,介绍了这一估计的统计特性和最优参数选择。讨论了基于受约束曲线拟合的正规互质因子参数辨识问题 ,给出了其解析解。最后介绍了模型集与控制器和闭环实验数据相匹配的一个充分必要条件。这一条件可表示为一个线性约束和一个复数向量的欧几里德范数。根据这一条件 ,讨论了随机框架下的模型集检验问题 ,给出了采样非伪概率的计算方法

Closed-loop identification and validation of normalized coprime factor perturbed model sets

System identification of robust control is an active research direction in the control research field. This paper surveys the identification and validation of model sets with normalized coprime factor perturbations. An analytic expression is given for the maximum likelihood estimate of normalized coprime factors' frequency response on the basis of closed loop experimental data. Its statistical properties and parameter selection issues are also surveyed. Parametric estimation is discussed based on constrained curve fitting with an analytic solution given for the optimal parameter. Finally, a necessary and sufficient condition is introduced for the unfalsification of a model set, which is expressed through a linear constraint and the Euclidean norm of a complex vector. Model set validation based on this condition is discussed for a stochastic framework with a summary of computation methods for the sample unfalsified probability.